Canonical correlation analysis on data with censoring and error information

Canonical Correlation Analysis With Low-Rank Learning for Image Representation

As a multivariate data analysis tool, canonical correlation analysis (CCA) has been widely used in computer vision and pattern recognition. However, CCA uses Euclidean distance as a metric, which is sensitive to noise or outliers in the data. Furthermore, CCA demands that the two training sets must have the same number of training samples, which limits the performance of CCA-based methods. To overcome these limitations of CCA, two novel canonical correlation learning methods based on low-rank learning are proposed in this paper for image representation, named robust canonical correlation analysis (robust-CCA) and low-rank representation canonical correlation analysis (LRR-CCA). By introducing two regular matrices, the training sample numbers of the two training datasets can be set as any values without any limitation in the two proposed methods. Specifically, robust-CCA uses low-rank learning to remove the noise in the data and extracts the maximization correlation features from the two learned clean data matrices. The nuclear norm and L₁ -norm are used as constraints for the learned clean matrices and noise matrices, respectively. LRR-CCA introduces low-rank representation into CCA to ensure that the correlative features can be obtained in low-rank representation. To verify the performance of the proposed methods, five publicly image databases are used to conduct extensive experiments. The experimental results demonstrate the proposed methods outperform state-of-the-art CCA-based and low-rank learning methods.

Multiview Latent Space Learning With Feature Redundancy Minimization

Multiview learning has received extensive research interest and has demonstrated promising results in recent years. Despite the progress made, there are two significant challenges within multiview learning. First, some of the existing methods directly use original features to reconstruct data points without considering the issue of feature redundancy. Second, existing methods cannot fully exploit the complementary information across multiple views and meanwhile preserve the view-specific properties; therefore, the degraded learning performance will be generated. To address the above issues, we propose a novel multiview latent space learning framework with feature redundancy minimization. We aim to learn a latent space to mitigate the feature redundancy and use the learned representation to reconstruct every original data point. More specifically, we first project the original features from multiple views onto a latent space, and then learn a shared dictionary and view-specific dictionaries to, respectively, exploit the correlations across multiple views as well as preserve the view-specific properties. Furthermore, the Hilbert-Schmidt independence criterion is adopted as a diversity constraint to explore the complementarity of multiview representations, which further ensures the diversity from multiple views and preserves the local structure of the data in each view. Experimental results on six public datasets have demonstrated the effectiveness of our multiview learning approach against other state-of-the-art methods.

Shared Autoencoder Gaussian Process Latent Variable Model for Visual Classification

Multiview learning reveals the latent correlation among different modalities and utilizes the complementary information to achieve a better performance in many applications. In this paper, we propose a novel multiview learning model based on the Gaussian process latent variable model (GPLVM) to learn a set of nonlinear and nonparametric mapping functions and obtain a shared latent variable in the manifold space. Different from the previous work on the GPLVM, the proposed shared autoencoder Gaussian process (SAGP) latent variable model assumes that there is an additional mapping from the observed data to the shared manifold space. Due to the introduction of the autoencoder framework, both nonlinear projections from and to the observation are considered simultaneously. Additionally, instead of fully connecting used in the conventional autoencoder, the SAGP achieves the mappings utilizing the GP, which remarkably reduces the number of estimated parameters and avoids the phenomenon of overfitting. To make the proposed method adaptive for classification, a discriminative regularization is embedded into the proposed method. In the optimization process, an efficient algorithm based on the alternating direction method and gradient decent techniques is designed to solve the encoder and decoder parts alternatively. Experimental results on three real-world data sets substantiate the effectiveness and superiority of the proposed approach as compared with the state of the art.

Multiview Privileged Support Vector Machines

Multiview learning (MVL), by exploiting the complementary information among multiple feature sets, can improve the performance of many existing learning tasks. Support vector machine (SVM)-based models have been frequently used for MVL. A typical SVM-based MVL model is SVM-2K, which extends SVM for MVL by using the distance minimization version of kernel canonical correlation analysis. However, SVM-2K cannot fully unleash the power of the complementary information among different feature views. Recently, a framework of learning using privileged information (LUPI) has been proposed to model data with complementary information. Motivated by LUPI, we propose a new multiview privileged SVM model, multi-view privileged SVM model (PSVM-2V), for MVL. This brings a new perspective that extends LUPI to MVL. The optimization of PSVM-2V can be solved by the classical quadratic programming solver. We theoretically analyze the performance of PSVM-2V from the viewpoints of the consensus principle, the generalization error bound, and the SVM-2K learning model. Experimental results on 95 binary data sets demonstrate the effectiveness of the proposed method.

Improved multi-view privileged support vector machine

Multi-view learning (MVL) concentrates on the problem of learning from the data represented by multiple distinct feature sets. The consensus and complementarity principles play key roles in multi-view modeling. By exploiting the consensus principle or the complementarity principle among different views, various successful support vector machine (SVM)-based multi-view learning models have been proposed for performance improvement. Recently, a framework of learning using privileged information (LUPI) has been proposed to model data with complementary information. By bridging connections between the LUPI paradigm and multi-view learning, we have presented a privileged SVM-based two-view classification model, named PSVM-2V, satisfying both principles simultaneously. However, it can be further improved in these three aspects: (1) fully unleash the power of the complementary information among different views; (2) extend to multi-view case; (3) construct a more efficient optimization solver. Therefore, in this paper, we propose an improved privileged SVM-based model for multi-view learning, termed as IPSVM-MV. It directly follows the standard LUPI model to fully utilize the multi-view complementary information; also it is a general model for multi-view scenario, and an alternating direction method of multipliers (ADMM) is employed to solve the corresponding optimization problem efficiently. Further more, we theoretically analyze the performance of IPSVM-MV from the viewpoints of the consensus principle and the generalization error bound. Experimental results on 75 binary data sets demonstrate the effectiveness of the proposed method; here we mainly concentrate on two-view case to compare with state-of-the-art methods.

Discriminative Feature Extraction by a Neural Implementation of Canonical Correlation Analysis

The canonical correlation analysis (CCA) aims at measuring linear relationships between two sets of variables (views) that can be used for feature extraction in classification problems with multiview data. However, the correlated features extracted by the CCA may not be class discriminative, since CCA does not utilize the class labels in its traditional formulation. Although there is a method called discriminative CCA (DCCA) that aims to increase the discriminative ability of CCA inspired from the linear discriminant analysis (LDA), it has been shown that the extracted features with this method are identical to those by the LDA with respect to an orthogonal transformation. Therefore, DCCA is simply equivalent to applying single-view (regular) LDA to each one of the views separately. Besides, DCCA and the other similar DCCA approaches have generalization problems due to the sample covariance matrices used in their computation, which are sensitive to outliers and noisy samples. In this paper, we propose a method, called discriminative alternating regression (D-AR), to explore correlated and also discriminative features. D-AR utilizes two (alternating) multilayer perceptrons, each with a linear hidden layer, learning to predict both the class labels and the outputs of each other. We show that the features found by D-AR on training sets significantly accomplish higher classification accuracies on test sets of facial expression recognition, object recognition, and image retrieval experimental data sets.

Data imputation through the identification of local anomalies

We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose: 1) a novel algorithm to efficiently separate, i.e., detect and localize, possible corruptions from a given suspicious data instance and 2) a maximum a posteriori estimator to impute the corrupted data. As a generalization to Euclidean distance, we also propose a novel distance measure, which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions. Our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted (clean) reference data set. Once each part is labeled as anomalous versus normal, the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed. Under a certain conditional independency structure assumed for the binary patterns, we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning. The proposed framework is tested over several well-known machine learning data sets with synthetically generated corruptions and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities. Our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions.